Cauchy's Mean Value Theorem

Cauchy's Mean Value Theorem

If $$f(x)$$ and $$g(x)$$ are continuous on $$[a,b]$$ and differentiable on $$(a,b)$$, with:

$$g'(x)\neq0$$

then there exists $$c\in(a,b)$$ such that:

$$\frac{f'(c)}{g'(c)}=\frac{f(b)-f(a)}{g(b)-g(a)}$$

provided:

$$g(b)\neq g(a)$$

Usage

- Used when two functions occur together and ordinary LMVT is not directly convenient.